Solve for Orthogonal Vectors b and c: Dot Product and Scalar Values Explained

In summary, to find the values of the scalar s for which the two vectors b and c are orthogonal, you need to calculate their dot product. Since the unit vectors are generally orthonormal, this means they are both orthogonal and have a unit magnitude. Therefore, the dot product equation should be \hat{x}-s^{2}\hat{y}. This will result in a scalar, not a vector quantity.
  • #1
krugertown
9
0
By evaluating their dot product, find the values of the scalar s for which the two vectors
b=[tex]\hat{x}[/tex]+s[tex]\hat{y}[/tex] and c=[tex]\hat{x}[/tex]-s[tex]\hat{y}[/tex]
are orthogonal.


I understand that for the two vecotrs to be perpindicular their dot product must be 0. however I am confused how to go about this problem as there are unit vectors.

Any ideas are appreciated. thanks!
 
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  • #2
gday krugertown

take the dot product & show me what you get...

the unit vectors are generally orthonormal - meaning orthogonal & unit magnitude, this should help...
 
  • #3
so something like [tex]\hat{x}[/tex]-s[tex]^{2}[/tex][tex]\hat{y}[/tex]?
 
  • #4
the results of a dot product should be a scalar not a vector quantity

try writing out the whole dot product
 

FAQ: Solve for Orthogonal Vectors b and c: Dot Product and Scalar Values Explained

1. What is a vector dot product?

A vector dot product, also known as a scalar product, is a mathematical operation that takes two vectors and returns a scalar value. It is calculated by multiplying the corresponding components of the two vectors and summing them up.

2. What is the purpose of a vector dot product?

The purpose of a vector dot product is to determine the degree of similarity or alignment between two vectors. It is also used to calculate the magnitude of one vector in the direction of another vector.

3. How is a vector dot product calculated?

To calculate a vector dot product, you multiply the corresponding components of the two vectors and then sum them up. For example, if you have two vectors, A = [2, 3, 5] and B = [4, 1, 2], the dot product would be 2*4 + 3*1 + 5*2 = 17.

4. What are some applications of vector dot product?

The vector dot product has various applications in mathematics, physics, and engineering. It is used in calculating work done by a force, determining the angle between two vectors, and finding the projection of one vector onto another.

5. Are there any properties of vector dot product?

Yes, there are several properties of vector dot product, including the commutative property (A * B = B * A), the distributive property (A * (B + C) = A * B + A * C), and the associative property (A * (B * C) = (A * B) * C).

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